The Department for Education insists it is allocating £5 billion over the course of this parliament to expand state primaries in England, with 238,344 places being added between 2010 and 2013 alone.

But the sheer demand has led to claims that some parents are forced to go to extreme lengths to get their preferred place.

This includes buying property or renting homes in catchment areas, befriending teachers at a chosen school and even getting children registered as having special needs to give them priority in the admissions process.

The disclosure was made as parents of more than 600,000 children find out which state primaries in England they have got into for September.

Reception class places will be allocated to four-year-olds as part of the first national “offer day” on Wednesday – when admissions are coordinated by all 152 local authorities in England. Previously, councils released allocations weeks or months apart.

The Government said the coordinated admissions system would make the process less "confusing and stressful” for parents this year.

Figures obtained by the Telegraph show:

– Some 18 per cent of children have missed out on their preferred school in Bristol this year – compared with just 14 per cent in 2013 – after demand for primary school places in the city soared by around a third in just six years;

– In Brighton, 17.5 per cent of children failed to get their first choice – up from 16 per cent a year ago – and one-in-20 pupils missed out on at least three schools;

– The number of children without their first choice increased from 10 to 12 per cent in Milton Keynes, from 13.5 to 15 per cent in Kent and from eight to nine per cent in Wiltshire;

– The London borough of Lambeth said that just over 21 per cent of pupils missed out on their first choice, up from 18 per cent a year ago, and around eight per cent failed to get any of their top three schools;

– East Sussex reported that fewer pupils secured their first choice schools this year while in the Midlands councils such as Derbyshire and Leicestershire also reported a drop.

But the squeeze on places was not seen in some other parts of the country.

Darlington, Stoke-on-Trent, Hull, Rutland and Windsor and Maidenhead all revealed an increase in the number of parents securing their first choice.

Councils such as Nottingham, Oldham and Rochdale said the proportion remained unchanged from last year.

Nationally, it is believed that around 80,000 children – one-in-eight – will miss out on their first choice school. Although comparable figures are not available for previous years, experts suggested that the rate is likely to be the highest ever seen.

The number is likely to be nearer a fifth across London and reach a third in some boroughs when full data for the capital is released on Wednesday.

A DfE spokesman said ensuring there were “enough school places for the growing population is one of the department’s top priorities”.

“We have more than doubled to £5 billion the funding available to local authorities to create new school places,” he said. “Nearly 80 per cent of new primary places created are in good or outstanding schools and our investment in the free schools programme is seeing 7 out of 10 new places created in areas of basic need.”

But David Simmonds, chairman of the Local Government Association’s children and young people board, said: “Despite all the work that’s gone on to create more school places, parents are still finding it a test to get the school of their choice.

“Because of the sheer number of children in the system, it is going to be more challenging to get the good local school that they want.”

Netmums, the parenting website, said that parents faced such competition for the best schools that “they will do almost anything to gain their child a place”.

Graham Jones, an education consultant who helps families fight admissions appeals, said: “Some parents go to incredible lengths to ensure a place at their preferred school. Religion, for example, can be highly contagious at the time of school applications, and moving into and out of certain catchment areas is popular.

“Others simply cheat the system using false addresses …. Such behaviours compound the pressures on good school places.”